Fundamentals of wavelet transformations

This chapter discusses various aspects of the wavelet transform when applied to continuous functions or signals. It may seem strange why this book has a chapter dealing with wavelet analysis for continuous functions, since, in practice most of us will be dealing with discretised functions or discrete signals. Here we think of a discrete signal being equivalent to a discrete near infrared spectrum, for example. Whilst continuous functions are not practical, they do assist substantially, in providing an understanding of the basic concepts and theories associated with wavelet analysis. A link actually emerges between wavelet transforms for continuous functions and discrete signals. Before we embark on a discussion on the fundamentals of wavelet transforms associated with continuous functions, we diverge momentarily to present a simple example and to provide motivation for the use of wavelet methods in signal analysis. This example does not use a continuous function, rather a sine curve which has been sampled 512 times.

N/A

Wavelets in Chemistry

N/A

978-0-444-50111-0

N/A

22

28